Here is a thread that I started on what seems to be a similar or the same issue. I took my car back to Lexus and they could not find anything wrong and, to be fair, the car drove flawlessly apart from the clicking noise when starting up from cold. This noise was never more than very faint and I came to regard it as simply a normal feature that I had become overly-sensitive about. Be aware that there is a known problem of a brief knock rather than a clicking noise at startup and this requires substantial rebuild work to resolve. However, from what I can deduce from the various threads on UK and US Lexus owner club websites, this is NOT the same problem that I had and, perhaps, you are having. My local Lexus dealer offered me a good deal on a new car after just over three years and put the old one on sale at quite a high price (it was in superb condition and very low mileage for the year) so I presume that they had no concerns about the engine (OK - maybe this is a naive presumption but I have found Lexus service pretty fair).
http://www.lexusownersclub.co.uk/forum/index.php?showtopic=54369